I have the following problem. I am trying to solve the following non-linear system of equations in MATLAB


where $\mathbf{b}$ (known) and $\mathbf{x}$ (to be found) are $N\times1$ column vectors, $\mathbf{A'A}$ (known) is a $N\times N$ cosine similarity matrix (symmetric positive definite). $\mathbf{I}$ is the identity matrix and $\mathbf{1}$ is a $N\times1$ vector of ones.

The obvious reference would seem this one: Solving Non Linear System of Equations with MATLAB

the problem is I'm not sure how to take the Jacobian. It seems to me that $\mathrm{diag}(\mathbf{x})$ and $(\mathbf{I+A'A})^{-1}$ should commute, so perhaps using that could simplify computation of the Jacobian.

But perhaps I'm wrong and that's not the way to go. Perhaps another possibility would be to write


make a guess for $\mathbf{x}_1$ and iterate till convergence. Any ideas? Thanks in advance!

  • $\begingroup$ take a look on the fsolve function $\endgroup$ – Thales Sep 9 at 20:32

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